The goal was to increase participation among people who otherwise wouldn’t have joined their 401(k)s. It's one of several steps that the government and private companies have taken to boost Americans’ dreary level of retirement saving.

On the surface, it appears to have worked. At companies with automatic enrollment, 77% of employees are in 401(k)s, according to the study. It’s 67% at companies without auto-enrollment.

But the analysis by the Center for Retirement Research at Boston College suggests that, in effect, the rest of us may be paying for it.

Companies typically make matching contributions to each employee’s 401(k) account. The match at companies without auto-enrollment is 3.5%, according to the study.

Companies with auto-enrollment pay only 3.2%. That might not sound like much of a difference, but it’s statistically significant, according to the study.

Why the lower rate? Because companies are trying to hold down their overall 401(k) costs, the study suggests.

Companies with higher levels of 401(k) participation have to shell out more in matching contributions. So they might be responding by reducing matching contributions.

In other words, employees who normally contribute to their 401(k)s might be subsidizing the participation of others.

“While auto-enrollment will increase saving for workers who would not have participated without it, those who would have participated on their own may end up saving less due to relatively low employer match rates,” the study concludes.